CN101627209A

CN101627209A - Oil pump rotor

Info

Publication number: CN101627209A
Application number: CN200780052084A
Authority: CN
Inventors: 沼波晃志; 小野寿
Original assignee: Aisin Seiki Co Ltd
Current assignee: Aisin Corp
Priority date: 2007-03-09
Filing date: 2007-12-05
Publication date: 2010-01-13
Anticipated expiration: 2027-12-05
Also published as: EP2123914B1; CN101627209B; WO2008111270A1; US8360762B2; JP5158448B2; EP2123914A4; JPWO2008111270A1; US20100129253A1; EP2123914A1; EP2123914B9

Abstract

An oil pump rotor used for a pump having an inner rotor that has n number (n: natural number) of outer teeth formed on it and also has an outer rotor having (n + 1) number of inner teeth formed on it and meshing with the outer teeth. The amount of discharge of the pump is increased without increasing the size of the rotor, and the oil pump rotor produces less pulsation. In the oil pump rotor, outer tooth shapes (U1in, U2in) are formed by circumferential deformations (U1, U2) and radial deformations (U1in, U2in) applied to tooth shapes (U'1, U'2) formed by a mathematicalcurve, and the circumferential and radial deformations are produced with the distance between the radius (RA1) of a tooth crest circle (A1) and the radius (RA2) of a tooth root circle (A2) maintained. Because of the circumferential deformations and radial deformations, the amount of discharge of the pump is increased without increasing the size of the rotor. Also, the number of the teeth is increased, so that the rotor has less pulsation and noise.

Description

Oil pump rotor

Technical Field

The present invention relates to an oil pump rotor that sucks and discharges fluid by utilizing a volume change of a chamber formed between an inner rotor and an outer rotor.

Background

The existing oil pump has: an inner rotor having n (n is a natural number) outer teeth; an outer rotor having n +1 inner teeth meshing with the outer teeth; and a housing that forms a suction port for sucking fluid and a discharge port for discharging fluid, wherein the oil pump rotates the inner rotor, the outer rotor is rotated by meshing the outer teeth with the inner teeth, and the fluid is sucked and discharged by utilizing the volume change of the plurality of chambers formed between the two rotors.

The chambers are partitioned by the outer teeth of the inner rotor and the inner teeth of the outer rotor contacting each other at the front and rear sides in the rotational direction thereof, respectively, and both side surfaces are partitioned by the housing, thereby constituting independent fluid transfer chambers. In addition, in the middle of the process of meshing the external teeth and the internal teeth, the volume of each chamber is expanded to suck the fluid when the chamber moves along the suction port after the volume becomes minimum, and the volume of each chamber is reduced to discharge the fluid when the chamber moves along the discharge port after the volume becomes maximum.

The oil pump having the above-described structure is small and simple in structure, and therefore is widely used for a lubricating oil pump, an automatic transmission oil pump, and the like of an automobile. When mounted on an automobile, an inner rotor is directly connected to a crankshaft of an engine as a drive unit of an oil pump, and the inner rotor is directly connected to the crankshaft and driven by the rotation of the engine.

For the oil pump, various oil pump types are currently disclosed, including: a type using an inner rotor and an outer rotor having tooth profiles formed by cycloid curves (see, for example, patent document 1); a type using an inner rotor having a tooth profile formed by an envelope of an arc group having a center on a trochoid curve (for example, see patent document 2); or a type in which an inner rotor and an outer rotor having tooth profiles formed by 2 arcs contacting each other are used (for example, see patent document 3); and an oil pump using the inner rotor and the outer rotor in which the tooth profiles of the above types are corrected.

Recently, as the valve system of an engine is changed or the output is increased, a piston cooling oil jet or the like is added, and the discharge capacity of an oil pump tends to increase. On the other hand, in order to reduce the friction of the engine from the viewpoint of saving fuel cost, the oil pump main body is required to be downsized and have a small diameter. In general, the number of teeth is reduced in order to increase the discharge amount of the oil pump, but in the oil pump having a small number of teeth, the discharge amount per chamber is large, so that pulsation becomes large, and there is a problem that noise is generated due to vibration of a pump body or the like.

As a method of reducing pulsation and suppressing noise, a method of increasing the number of teeth is generally employed, but in theory, in a tooth profile formed by a cycloid curve or the like, if the number of teeth increases, the discharge amount decreases, so in order to secure a necessary discharge amount, it is necessary to increase the outer diameter of the rotor or increase the thickness in the axial direction, which results in problems such as an increase in size, an increase in weight, and an increase in friction.

Patent document 1: japanese patent laid-open publication No. 2005-076563

Patent document 2: japanese laid-open patent publication No. H09-256963

Patent document 3: japanese laid-open patent publication No. 61-008484

Disclosure of Invention

The present invention has been made in view of the above problems, and an object of the present invention is to provide an oil pump rotor that increases the discharge amount without increasing the size of the rotor, and has small pulsation and low noise.

An oil pump rotor for use in an oil pump, the oil pump having: an inner rotor having n (n is a natural number) outer teeth; an outer rotor that forms n +1 inner teeth that mesh with the outer teeth; and a housing which forms a suction port for sucking fluid and a discharge port for discharging fluid, and sucks and discharges the fluid by using a volume change of a chamber formed between tooth surfaces of the two rotors when the two rotors are meshed with each other to rotate, thereby conveying the fluid₁Radius R of_A1And the tooth space circle A₂Radius R of_A2The distance between them.

This makes it possible to increase the discharge amount without increasing the size of the rotor, and to provide a low-noise oil pump rotor with small pulsation.

The mathematical curve referred to herein is a curve expressed by a mathematical function, and preferable examples thereof include a cycloid curve, an envelope curve of a group of arcs having a center on a trochoid curve, or an arc curve formed by 2 arcs connecting a tooth top portion and a tooth space portion to each other.

In addition, as one of preferred embodiments of the inner rotor, there is an inner rotor in which the deformation in the circumferential direction satisfies R_A1＞R_C1＞R_A2Radius R of_C1Circle C of₁At a1 st deformation rate γ₁Is deformed while being on the circle C₁At a2 nd deformation rate γ₂The deformation is carried out, and the deformation is carried out,

said deformation in the radial direction being such as to satisfy R_A1＞R_D1≥R_C1≥R_D2＞R_A2Radius of (2)R_D1Circle D of₁In the case of the outer side deformation, the tooth crest shape is defined as a curve formed by the equations (1) to (4) and has a radius R_D2Circle D of₂In the case of the inner deformation of (3), the curve formed by equations (5) to (8) is defined as a spline shape.

R₁₂＝(X₁₁ ²+Y₁₁ ²)^1/2Formula (1)

θ₁₂＝arccos(X₁₁/R₁₂) Formula (2)

X₁₂＝{(R₁₂-R_D1)×β₁₀+R_D1}×cos θ₁₂Formula (3)

Y₁₂＝{(R₁₂-R_D1)×β₁₀+R_D1}×sin θ₁₂Formula (4)

Wherein,

(X₁₁，Y₁₁) Is the coordinate of the tooth crest shape before radial deformation,

(X₁₂，Y₁₂) Is the coordinate of the tooth crest shape after the radial deformation,

R₁₂from the center of the inner rotor to the coordinates (X)₁₁，Y₁₁) The distance of (a) to (b),

θ₁₂is through the center and coordinates (X) of the inner rotor₁₁，Y₁₁) Is at an angle to the X-axis,

β₁₀is a correction factor for the deformation.

R₂₂＝(X₂₁ ²+Y₂₁ ²)^1/2Formula (5)

θ₂₂＝arccos(X₂₁/R₂₂) Formula (6)

X₂₂＝{R_D2-(R_D2-R₂₂)×β₂₀}×cos θ₂₂Formula (7)

Y₂₂＝{R_D2-(R_D2-R₂₂)×β₂₀}×sin θ₂₂Formula (8)

Wherein,

(X₂₁，Y₂₁) Is the coordinate of the tooth socket shape before radial deformation,

(X₂₂，Y₂₂) Is the coordinate of the tooth socket shape after being deformed in the radial direction,

R₂₂from the center of the inner rotor to the coordinates (X)₂₁，Y₂₁) The distance of (a) to (b),

θ₂₂is through the center and coordinates (X) of the inner rotor₂₁，Y₂₁) Is at an angle to the X-axis,

β₂₀is a correction factor for the deformation.

In another preferred embodiment of the inner rotor, there is an inner rotor having a reference circle C passing through a tooth tip side meshing point a of the inner rotor and the outer rotor_αThe tooth crest portion of the outer side of the tooth is deformed in the radial direction at a deformation rate ε satisfying 0 < ε < 1.

This makes it possible to keep the gap between the tooth tips between the inner rotor and the outer rotor constant, thereby further reducing the pulsation of the oil discharged from the oil pump.

In particular, as one of preferable embodiments of the present invention, there is an embodiment in which a cycloid curve is used as the mathematical curve and the inner rotor deformed in the circumferential direction and the radial direction and the outer rotor engaged with the inner rotor are formed in a tooth shape formed by the cycloid curve, and the outer tooth shape of the inner rotor is formed by a base circle having a radius R_aThe radius of the outer rolling circle is R_a1The radius of the inner rolling circle is R_a2The tooth profile of the cycloid curve is formed by performing the deformation in the circumferential direction and the deformation in the radial direction, and when the deformation in the circumferential direction is performed, a base circle of the cycloid curve is defined as the circle C₁，

The inner tooth shape of the outer rotor engaged with the inner rotor is formed by pairing a base circle with radius of R_bThe radius of the outer rolling circle is R_b1The radius of the inner rolling circle is R_b2The tooth profile of the cycloid curve of (1) is formed by deforming in the circumferential direction and deforming in the radial direction, and the tooth space circle B is maintained when the tooth profile is deformed in the circumferential direction₁Radius R of_B1And addendum circle B₂Radius R of_B2The distance between the two or more of the two or more,

here, the deformation of the outer rotor in the circumferential direction is at a radius R_bIs deformed outside the base circle of (1), at a 3 rd deformation rate delta₃Deformation is carried out while at radius R_bIs deformed at the 4 th deformation rate delta₄The deformation is carried out and, moreover,

the radial deformation of the outer rotor satisfies R_B1＞R_D3≥R_b≥R_D4＞R_B2Radius R of_D3Circle D of₃In the case of the outer deformation of (2), the curve formed by the equations (9) to (12) is a tooth space shape at the radius R_D4Circle D of₄In the case of the inner side deformation of (2), the curve formed by the equations (13) to (16) is defined as the tooth crest shape,

also, the outer rotor and the inner rotor satisfy the relationship of equations (17) to (21).

R₃₂＝(X₃₁ ²+Y₃₁ ²)^1/2Formula (9)

θ₃₂＝arccos(X₃₁/R₃₂) Formula (10)

X₃₂＝{(R₃₂-R_D3)×β₃₀+R_D3}×cos θ₃₂Formula (11)

Y₃₂＝{(R₃₂-R_D3)×β₃₀+R_D3}×sin θ₃₂Formula (12)

Wherein,

(X₃₁，Y₃₁) Is the coordinate of the tooth socket shape before radial deformation,

(X₃₂，Y₃₂) Is the coordinate of the tooth socket shape after being deformed in the radial direction,

R₃₂is from the center of the outer rotor to the coordinate (X)₃₁，Y₃₁) The distance of (a) to (b),

θ₃₂is through the center and coordinate (X) of the outer rotor₃₁，Y₃₁) Is at an angle to the X-axis,

β₃₀is a correction factor for the deformation.

R₄₂＝(X₄₁ ²+Y₄₁ ²)^1/2Formula (13)

θ₄₂＝arccos(X₄₁/R₄₂) Formula (14)

X₄₂＝{R_D4-(R_D4-R₄₂)×β₄₀}×cos θ₄₂Formula (15)

Y₄₂＝{R_D4-(R_D4-R₄₂)×β₄₀}×sin θ₄₂Formula (16)

Wherein,

(X₄₁，Y₄₁) Is the coordinate of the tooth crest shape before radial deformation,

(X₄₂，Y₄₂) Is a tooth deformed radiallyThe coordinates of the shape of the roof,

R₄₂is from the center of the outer rotor to the coordinate (X)₄₁，Y₄₁) The distance of (a) to (b),

θ₄₂is through the center and coordinate (X) of the outer rotor₄₁，Y₄₁) Is at an angle to the X-axis,

β₄₀is a correction factor for the deformation.

In addition, the first and second substrates are,

R_a＝n×(R_a1×γ_a+R_a2×γ₂) Formula (17)

R_b＝(n+1)×(R_b1×δ₃+R_b2×δ₄) Formula (18)

R_b＝R_a+R_a1+R_a2+ H1 type (19)

R_b2＝R_a2+ H2 type (20)

e₁₀＝R_a1+R_a2+ H3 type (21)

Wherein,

e₁₀is the distance (eccentricity) between the center of the inner rotor and the center of the outer rotor,

h1, H2, and H3 are correction values for rotating the outer rotor with a gap.

In each of the above configurations, the outer tooth shape of the inner rotor is formed by deforming the tooth profile formed by the mathematical curve in the circumferential direction and deforming the tooth profile in the radial direction.

That is, it is possible to obtain an oil pump rotor that is capable of supplying oilThe oil pump is used in a pump, and comprises: an inner rotor having n (n is a natural number) outer teeth; an outer rotor that forms n +1 inner teeth that mesh with the outer teeth; and a housing which forms a suction port for sucking fluid and a discharge port for discharging fluid, and which sucks and discharges fluid by using a volume change of a chamber formed between tooth surfaces of the two rotors when the two rotors are engaged and rotated, thereby transferring the fluid, wherein the external tooth shape of the inner rotor is formed by maintaining an addendum circle A of a tooth profile shape formed by a mathematical curve₁Radius R of_A1And the tooth space circle A₂Radius R of_A2The distance between the two members is formed by performing compression deformation in the circumferential direction.

Thus, the discharge amount can be increased while the diameter of the rotor is ensured, and a low-noise oil pump rotor with small pulsation can be provided.

In addition, as a preferred embodiment of the outer rotor that meshes with an inner rotor formed by deforming the inner rotor in the circumferential direction and the radial direction or by compressing and deforming the inner rotor in the circumferential direction with respect to the tooth profile formed by the mathematical curve, there is an outer rotor having a tooth profile formed in the following manner:

an envelope formed by revolving the inner rotor at an angular velocity ω around a circle F having a radius e equal to a predetermined distance e and centered at a position separated from the center by the predetermined distance e, and rotating the inner rotor at an angular velocity ω/n which is 1/n times the angular velocity ω of the revolution in a rotational direction opposite to the revolving direction,

an angle of a center of the inner rotor when the revolution is started as viewed from a center of the circle F is set to a revolution angle 0 direction, at least a vicinity of an intersection of the envelope and an axis in the revolution angle 0 direction is deformed in an outer diameter direction, and a vicinity of an intersection of the envelope and an axis in a revolution angle pi/(n +1) direction of the inner rotor is deformed in an outer diameter direction,

extracting a portion included in a region defined by a revolution angle of 0 or more and pi/(n +1) or less as a partial envelope,

a correction portion envelope formed by cutting off a portion extending out of the region while rotating the partial envelope by a slight angle α in the revolution direction with the center of the circle F as a base point and connecting a gap generated between the partial envelope and an axis in the revolution angle 0 direction,

the correction partial envelop line is copied in line symmetry relative to the axis of the revolution angle 0 direction to form a partial tooth shape,

further, the partial tooth profile is rotationally transferred at an angle of 2 pi/(n +1) with the center of the circle F as a base point, thereby forming a tooth profile shape.

Accordingly, the inner rotor formed by deforming the teeth in the circumferential direction and the radial direction or by compressing and deforming the teeth in the circumferential direction, which are formed by the mathematical curve, can be easily formed into the outer rotor smoothly meshing with the inner rotor and rotating.

Drawings

Fig. 1 is an explanatory diagram illustrating a deformation of an inner rotor in the circumferential direction in the present invention.

Fig. 2 is an explanatory diagram illustrating a radial deformation of the inner rotor in the present invention.

Fig. 3 is a diagram showing an oil pump having a tooth profile formed by a deformed cycloid curve.

Fig. 4 is an explanatory diagram (deformation in the circumferential direction) for forming the inner rotor of fig. 3.

Fig. 5 is an explanatory view (deformation in the radial direction) for forming the inner rotor of fig. 3.

Fig. 6 is an explanatory diagram (deformation in the circumferential direction) for forming the outer rotor of fig. 3.

Fig. 7 is an explanatory view (deformation in the radial direction) for forming the outer rotor of fig. 3.

Fig. 8 is an explanatory diagram showing a tooth profile shape formed by an envelope of an arc group having a center on a trochoid curve.

Fig. 9 is an explanatory diagram showing a tooth profile shape formed by an arc curve formed by 2 arcs connecting the tooth top portion and the tooth space portion to each other.

Fig. 10 is a diagram showing a meshing region between the inner rotor and the outer rotor.

Fig. 11 is an explanatory diagram showing a second modification in the radial direction.

Fig. 12 is a graph showing a relationship between the rotation angle of the inner rotor and the tip clearance.

Fig. 13 is an explanatory diagram for forming an outer rotor.

Detailed Description

Fig. 1 and 2 are schematic diagrams illustrating a process for forming the tooth profile (external tooth profile) of the inner rotor in the present invention by deforming a mathematical curve in the circumferential direction and deforming it in the radial direction. Note that, of the external teeth formed on the inner rotor in fig. 1 and 2, 1 tooth top portion and tooth groove portion are shown, and other teeth are omitted, but it goes without saying that the same modification is performed for all the teeth.

Fig. 1 is a diagram showing deformation in the circumferential direction applied to a tooth profile shape formed of a mathematical curve. In fig. 1, the tooth crest shape U 'is a tooth profile shape U' formed by a mathematical curve₁' and gullet shape U₂' indicated by a dotted line, so as to conform to the shape of the tooth tip U₁' inscribed addendum circle A₁Has a radius of R_A1To make the shape of gullet U₂' circumscribed tooth space circle A₂Has a radius of R_A2. In addition, byAnd satisfy R_A1＞R_C1＞R_A2Circle C of₁Radius R of_C1The tooth crest shape U is formed by the tooth profile shape U' positioned at the outer side₁'the tooth profile U' on the inner side forms a tooth space U₂’。

In addition, the addendum circle A is maintained₁Radius R of_A1And the tooth space circle A₂Radius R of_A2Distance (R) therebetween_A1-R_A2) At the same time, the tooth profile U is deformed in the circumferential direction at a predetermined deformation ratio to obtain the deformed tooth profile U. In FIG. 1, the radius is R_C1Circle C of₁Outer side of (i.e. tooth crest shape U)₁' in case of deformation, at the 1 st deformation rate γ₁Deforming so that the radius is R_C1Circle C of₁Inner side of (2), i.e. gullet shape U₂' in case of deformation, at the 2 nd deformation ratio γ₂Deformation is performed. Here, the deformation ratio is a ratio of an angle formed by a ray connecting the center O of the inner rotor and one end of a curve forming a tooth crest shape (tooth space shape) and a ray connecting the center O of the inner rotor and the other end of the curve before and after deformation. In FIG. 1, for the addendum shape U₁The angle before deformation is theta₁', after deformation is theta₁Therefore, the addendum shape U₁At a1 st deformation ratio gamma₁＝θ₁/θ₁' deformed. Similarly, for gullet shape U₂The angle before deformation is theta₂', after deformation is theta₂Thus, the gullet shape U₂At a2 nd deformation ratio gamma₂＝θ₂/θ₂' deformed. By the above-described deformation in the circumferential direction, a deformed tooth profile U (tooth crest U) can be obtained₁And gullet shape U₂)。

In addition, the transformation formula for obtaining the tooth profile U deformed in the circumferential direction from the tooth profile U' is obtained by using the deformation ratio γ₁Or gamma₂It can be simply expressed as follows. I.e. for that in fig. 1Tooth top shape U₁' coordinate (X)₁₀，Y₁₀) If the distance between the coordinate and the center O of the inner rotor is R, the angle formed by the straight line passing through the coordinate and the center O of the inner rotor and the X axis is theta₁₁Then, it can be expressed as (Rcos θ)₁₁，Rsinθ₁₁) So that the tooth crest shape U after deformation in the circumferential direction₁Corresponding coordinate (X)₁₁，Y₁₁) Using the deformation ratio gamma₁Can be expressed as (Rcos (theta))₁₁×γ₁)，Rsin(θ₁₁×γ₁))＝(Rcosθ₁₂，Rsinθ₁₂). Here, θ₁₂Is through the center O and coordinate (X) of the inner rotor₁₁，Y₁₁) Is at an angle to the X-axis. The deformation ratio γ can be used similarly for the spline shape₂And (4) performing representation.

If the number of teeth (outer teeth) of the inner rotor before and after the deformation in the circumferential direction is n ' and n (n ' and n are natural numbers), the following formula n ' × (θ)₁’+θ₂’)＝n×(θ₁+θ₂) This is true.

As described above, the addendum circle A is maintained₁Radius R of_A1And the tooth space circle A₂Radius R of_A2The deformation in the circumferential direction performed while maintaining the distance is performed in accordance with the change in the vertex angle with respect to the tooth profile included in the sector region having the center O of the rotor as the vertex. The deformation ratio γ, which is a ratio of the vertex angle before and after deformation, is an enlarged deformation when γ > 1 and a compression deformation when γ < 1.

Fig. 2 is a view showing the deformation of the tooth profile U in the radial direction after the above-described deformation in the circumferential direction is applied to the tooth profile U' formed by a mathematical curve. An example of such radial deformation is shown below. This is when R is satisfied_A1＞R_D1≥R_C1≥R_D2＞R_A2Has a radius of R_D1Circle D of₁Will be formed by the formulae (1) to (4)The curve of (a) is taken as the tooth crest shape and has a radius of R_D2Circle D of₂In the case of the inner deformation of (3), the curve formed by equations (5) to (8) is defined as a spline shape.

R₁₂＝(X₁₁ ²+Y₁₁ ²)^1/2Formula (1)

θ₁₂＝arccos(X₁₁/R₁₂) Formula (2)

X₁₂＝{(R₁₂-R_D1)×β₁₀+R_D1}×cos θ₁₂Formula (3)

Y₁₂＝{(R₁₂-R_D1)×β₁₀+R_D1}×sin θ₁₂Formula (4)

Wherein,

β₁₀is a correction factor for the deformation.

R₂₂＝(X₂₁ ²+Y₂₁ ²)^1/2Formula (5)

θ₂₂＝arccos(X₂₁/R₂₂) Formula (6)

X₂₂＝{R_D2-(R_D2-R₂₂)×β₂₀}×cos θ₂₂Formula (7)

Y₂₂＝{R_D2-(R_D2-R₂₂)×β₂₀}×sin θ₂₂Formula (8)

Wherein,

β₂₀is a correction factor for the deformation.

FIG. 2(a) shows a tooth crest shape U formed by the above-mentioned deformation in the circumferential direction₁(shown by a dotted line), a view of the case where the radial deformation is performed using the above-described equations (1) to (4), and the tooth crest shape U is obtained by the radial deformation_1in. FIG. 2(b) shows a spline shape U formed by the above-mentioned deformation in the circumferential direction₂(shown by a dotted line), a view of the case where the radial deformation is performed by using the above equations (5) to (8), and the radial deformation is used to obtain the tooth space shape U_2in. That is, in the above expressions (1) to (8), the tooth crest shape U before the radial deformation₁And gullet shape U₂Respectively in the form of (X)₁₁，Y₁₁)、(X₂₁，Y₂₁) Showing the tooth crest shape U after radial deformation_1inAnd gullet shape U_2inRespectively in the form of (X)₁₂，Y₁₂)、(X₂₂，Y₂₂) And (4) showing. Wherein is located at R_D1And R_D2The portion between the first and second members is not deformed by the deformation in the radial direction.

As described above, the tooth profile U of the inner rotor in the present invention can be obtained by performing the above-described deformation in the circumferential direction and the deformation in the radial direction on the tooth profile U' formed by the mathematical curve_in(tooth tip shape U)_1inAnd gullet shape U_2in)。

In addition, in particular, for the correction coefficient β for the deformation in the radial direction₁₀、β₂₀In addition to the value larger than 1, as shown in fig. 2, a value smaller than 1 may be used, but in the above case, a value is selected which is equal to the radius R of the inner rotor having the tooth profile shape which is formed by the mathematical curve and has the same number of teeth n as the number of teeth of the inner rotor in the present invention_C1Circle C of₁In the inner rotor having n tooth crest shapes and n tooth trough shapes formed by the mathematical curve as a reference, at least one of the tooth crest shapes and the tooth trough shapes is increased in the radial direction (the outer diameter direction in the case of the tooth crest shape and the inner diameter direction in the case of the tooth trough shape) to increase the discharge amount.

In addition, regarding the change in the circumferential direction, in fig. 1 and 2, the number of teeth of the inner rotor before and after the deformation in the circumferential direction is represented by n 'and n, respectively, and the case where n' < n, that is, the deformation ratio γ is shown₁、γ₂All of them are less than 1, but the deformation ratio γ may be set to₁、γ₂Greater than 1, and is subject to magnification deformation (i.e., n' > n). In this case, as described above, the correction coefficient β for the deformation in the radial direction is set to be smaller₁₀、β₂₀In the present invention, the value is selected such that at least one of the tooth top shape and the tooth space shape is increased in the radial direction (the outer diameter direction in the case of the tooth top shape and the inner diameter direction in the case of the tooth space shape) so as to increase the discharge amount, as compared with the inner rotor having the tooth form shape which is formed by the above mathematical curve and has the same number of teeth n as the number of teeth of the inner rotor.

In fig. 1 and 2, the deformation is performed in the radial direction after the deformation is performed in the circumferential direction, but the deformation is performed in the radial directionAfter the radial deformation, the deformation may be performed in the circumferential direction while maintaining the distance between the radius of the addendum circle and the radius of the slot circle. In fig. 1, R may not be set_C1And the tooth crest shape and the tooth groove shape are deformed at the same deformation rate. Similarly, the outer rotor may be deformed in the circumferential direction or in the radial direction, and may have a tooth shape (inner tooth shape) that appropriately meshes with the inner rotor.

[ tooth shape made of deformed cycloid curve ]

Next, the tooth profile of the inner rotor and the outer rotor when a cycloid curve is used as the mathematical curve will be described in detail with reference to fig. 3 to 7.

The oil pump shown in fig. 3 is an embodiment in which deformation in the circumferential direction and deformation in the radial direction are performed on a tooth profile formed of a cycloid curve. The oil pump has: an inner rotor 10 forming 9 outer teeth 11; an outer rotor 20 having 10 internal teeth 21 engaged with the external teeth 11 of the inner rotor 10; and a housing 50 which forms a suction port 40 for sucking fluid and a discharge port 41 for discharging fluid, and sucks and discharges the fluid by utilizing a volume change of a chamber 30 formed between tooth surfaces of the two rotors when the two rotors are engaged and rotated, thereby transferring the fluid.

Fig. 4 and 5 are explanatory views for forming the inner rotor 10 of fig. 3. Fig. 4 shows a tooth profile formed by deforming a tooth profile formed by a cycloid curve in the circumferential direction, which corresponds to fig. 1, fig. 5 shows a tooth profile formed by deforming the tooth profile in the circumferential direction, which corresponds to fig. 2, and a tooth profile formed by deforming the tooth profile in the radial direction.

In fig. 4, the tooth profile U is formed by a cycloid curve_C' middle, tooth top shape U_1C' and gullet shape U_2C' is shown in dotted lines. In addition, if the base radius of the cycloid curve is R_aThe radius of the outer rolling circle is set to R_a1The radius of the inner rolling circle is setIs R_a2The tooth top shape U_1C' inscribed addendum circle A₁May be represented by R_a+2R_a1Indicating the form U of the gullet_2C' circumscribed tooth space circle A₂May be represented by R_a-2R_a2And (4) showing. In addition, a circle C indicating a boundary between the tooth top portion and the tooth space portion in fig. 1₁Radius R of_C1In this FIG. 4, the base radius R_a. I.e. with a radius R_a1The cycloidal curve of the external rolling circle forms an addendum shape U_1C', consisting of a radius R_a2The cycloidal curve of the inner rolling circle forms a tooth groove shape U_2C’。

Further, the base radius is R_aThe radius of the outer rolling circle is R_a1The radius of the inner rolling circle is R_a2The coordinates of the known cycloid curve can be expressed by the following equation (the drawing is omitted).

X₁₀＝(R_a+R_a1)×cos θ₁₀

-R_a1×cos〔{(R_a+R_a1)/R_a1}×θ₁₀Formula (31)

Y₁₀＝(R_a+R_a1)×sin θ₁₀

-R_a1×sin〔{(R_a+R_a1)/R_a1}×θ₁₀Formula (32)

X₂₀＝(R_a-R_a2)×cos θ₂₀

+R_a2×cos〔{(R_a2-R_a)/R_a2}×θ₂₀Formula (33)

Y₂₀＝(R_a-R_a2)×sin θ₂₀

+R_a2×sin〔{(R_a2-R_a)/R_a2}×θ₂₀Formula (34)

R_a＝n×(R_a1+R_a2) Formula (35)

Here, the center O of the inner rotor 10 is passed through₁Is the X-axis such that the straight line orthogonal to the X-axis passes through the center O of the inner rotor 10₁Is the Y axis, and in the formulae (31) to (35), θ₁₀Is through the center of the outer rolling circle and the center O of the inner rotor 10₁Angle theta of the straight line of (a) with the X-axis₂₀Is through the center of the inner rolling circle and the center O of the inner rotor 10₁Angle (X) to the X-axis₁₀，Y₁₀) Is the coordinate of the cycloid curve formed by the outer rolling circle, (X)₂₀，Y₂₀) Is the coordinate of the cycloid curve formed by the inner rolling circle.

In addition, the addendum circle A is maintained₁Radius R of_a+2R_a1And the tooth space circle A₂Radius R of_a-2R_a2While the tooth profile U is deformed at a predetermined deformation rate in the circumferential direction_C. In FIG. 4, at the base radius R_aOutside, i.e. tooth tip shape U_1CIn the case of deformation, the 1 st deformation rate γ₁＝θ_1C/θ_1C' deformation is carried out at the base radius R_aInside of (2), i.e. gullet shape U_2CIn the case of' deformation, at a2 nd deformation rate γ₂＝θ_2C/θ_2C' deformation is performed. In addition, with respect to the angle θ_1CEtc. are as described above. By the above-described deformation in the circumferential direction, the deformed tooth profile U can be obtained_C(tooth tip shape U)_1CAnd gullet shape U_2C). If the numbers of teeth of the inner rotor before and after the deformation in the circumferential direction are n 'and n, respectively, the relational expression n' × (θ)_1C’+θ_2C’)＝n×(θ_1C+θ_2C) This is true.

Here for forming a tooth profile U_C' obtaining a tooth-like shape U_CBy using the transformation of (1), by using the deformation ratio γ₁Or gamma₂And can be simply expressed. Example (b)For example, the tooth crest shape is the tooth crest shape U before deformation in the circumferential direction_1C' is the cycloid curve (X)₁₀，Y₁₀) Tooth crest shape U after deformation in circumferential direction_1CCoordinate (X) of₁₁，Y₁₁) These compounds can be represented by the following formulae (36) to (39).

R₁₁＝(X₁₀ ²+Y₁₀ ²)^1/2Formula (36)

θ₁₁＝arccos(X₁₀/R₁₁) Formula (37)

X₁₁＝R₁₁×cos(θ₁₁×γ₁) Formula (38)

Y₁₁＝R₁₁×sin(θ₁₁×γ₁) Formula (39)

Here, R is₁₁Is from the center O of the inner rotor₁To the coordinate (X)₁₀，Y₁₀) A distance of (a), theta₁₁Is through the center O of the inner rotor₁And coordinates (X)₁₀，Y₁₀) Is at an angle to the X-axis.

Due to the tooth socket shape U after deformation in the circumferential direction_2CCoordinate (X) of₂₁，Y₂₁) The shape of the tooth space before the deformation in the circumferential direction may be determined according to the shape of the tooth space U before the deformation in the circumferential direction_2C', i.e. the cycloid curve (X) described above₂₀，Y₂₀) By using the deformation ratio gamma₂Since it is also easy to obtain, it is omitted here.

Next, the tooth profile U after the deformation in the circumferential direction is treated_CThe deformation in the radial direction as shown in fig. 5 is performed. First, will be satisfying R_a+2R_a1＞R_D1≥R_a≥R_D2＞R_a-2R_a2Radius R of_D1Circle D of₁The outer side (tooth top side) of (b), as shown in fig. 5(a), coordinates (X) represented by the following formulae (1) to (4)₁₂，Y₁₂) The formed curve is the tooth crest shape after deformation.

R₁₂＝(X₁₁ ²+Y₁₁ ²)^1/2Formula (1)

θ₁₂＝arccos(X₁₁/R₁₂) Formula (2)

X₁₂＝{(R₁₂-R_D1)×β₁₀+R_D1}×cos θ₁₂Formula (3)

Y₁₂＝{(R₁₂-R_D1)×β₁₀+R_D1}×sin θ₁₂Formula (4)

Here, (X)₁₁，Y₁₁) Is in the shape of tooth top U before radial deformation_1C(X) of (C)₁₂，Y₁₂) Is in the shape of tooth top U after being deformed in radial direction_1inCoordinate of (A), R₁₂Is from the center O of the inner rotor₁To the coordinate (X)₁₁，Y₁₁) A distance of (a), theta₁₂Is through the center O of the inner rotor₁And coordinates (X)₁₁，Y₁₁) Angle beta of the straight line of (A) to the X-axis₁₀Is a correction factor for the deformation.

In addition, R will be satisfied_a+2R_a1＞R_D1≥R_a≥R_D2＞R_a-2R_a2Radius R of_D2Circle D of₂Inner side (tooth groove side) of (b), as shown in fig. 5(b), coordinates (X) represented by the following formulas (5) to (8)₂₂，Y₂₂) The formed curve is the tooth space shape after deformation.

R₂₂＝(X₂₁ ²+Y₂₁ ²)^1/2Formula (5)

θ₂₂＝arccos(X₂₁/R₂₂) Formula (6)

X₂₂＝{R_D2-(R_D2-R₂₂)×β₂₀}×cos θ₂₂Formula (7)

Y₂₂＝{R_D2-(R_D2-R₂₂)×β₂₀}×sin θ₂₂Formula (8)

Here, (X)₂₁，Y₂₁) Is in the form of tooth socket U before radial deformation_2C(X) of (C)₂₂，Y₂₂) Is in the form of tooth socket U after being deformed radially_2inCoordinate of (A), R₂₂Is from the center O of the inner rotor₁To the coordinate (X)₂₁，Y₂₁) A distance of (a), theta₂₂Is through the center O of the inner rotor₁And coordinates (X)₂₁，Y₂₁) Angle beta of the straight line of (A) to the X-axis₂₀Is a correction factor for the deformation.

That is, the tooth tip shape U is formed by deformation in the radial direction as shown in FIG. 5(a)_1CObtain the tooth top shape U_1inBy the deformation in the radial direction shown in FIG. 5(b), the spline shape U is formed_2CObtain the tooth socket shape U_2in. As described above, by performing the above-described deformation in the circumferential direction and the deformation in the radial direction on the tooth profile U' formed of the cycloid curve, the tooth profile U of the inner rotor formed of the deformed cycloid curve can be obtained_in(tooth tip shape U)_1inAnd gullet shape U_2in) The outer teeth shape of the inner rotor 10 shown in fig. 3 may be formed.

On the other hand, fig. 6 and 7 are explanatory views for forming the outer rotor 20 of fig. 3. Fig. 6 shows a tooth profile formed by deforming a tooth profile formed by a cycloid curve in the circumferential direction, which corresponds to the case of applying the above-described fig. 1 to the outer rotor, and fig. 7 shows a tooth profile formed by deforming the tooth profile in the circumferential direction, which corresponds to the case of applying the above-described fig. 2 to the outer rotor.

In fig. 6, the tooth profile U is formed by a cycloid curve_C' middle, gullet shape U_3C' and tooth tip shape U_4C' is shown in dotted lines. In addition, if the base circle of the cycloid curve is halvedDiameter is set as R_bThe radius of the outer rolling circle is set to R_b1The radius of the inner rolling circle is set to R_b2Then form a U with the tooth socket_3C' inscribed tooth space circle B₁May be represented by R_b+2R_b1Showing, the tooth crest shape U_4C' circumscribed addendum circle B₂May be represented by R_b-2R_b2And (4) showing. In addition, a circle C in fig. 1 indicating a boundary between the tooth top portion and the tooth space portion₁Radius R of_C1In this FIG. 6, the base radius R_b. I.e. with a radius R_b1The cycloidal curve of the outer rolling circle forms a tooth groove shape U_3C', consisting of a radius R_b2The cycloidal curve of the inner rolling circle forms the tooth crest shape U_4C’。

Further, the base radius is R_bThe radius of the outer rolling circle is R_b1The radius of the inner rolling circle is R_b2The coordinates of the known cycloid curve can be expressed by the following equation (the drawing is omitted).

X₃₀＝(R_b+R_b1)cos θ₃₀

-R_b1×cos〔{(R_b+R_b1)/R_b1}×θ₃₀Formula (41)

Y₃₀＝(R_b+R_b1)sin θ₃₀

-R_b1×sin〔{(R_b+R_b1)/R_b1}×θ₃₀Formula (42)

X₄₀＝(R_b-R_b2)cos θ₄₀

+R_b2×cos〔{(R_b2-R_b)/R_b2}×θ₄₀Formula (43)

Y₄₀＝(R_b-R_b2)sin θ₄₀

+R_b2×sin〔{(R_b2-R_b)/R_b2}×θ₄₀Formula (44)

R_b＝(n+1)×(R_b1+R_b2) Formula (45)

Here, the center O of outer rotor 20 is passed through₂Is the X-axis, such that a line orthogonal to the X-axis passes through the center O of outer rotor 20₂Is the Y axis, and in the formulae (41) to (45), θ₃₀Is through the center of the outer rolling circle and the center O of outer rotor 20₂Angle theta of the straight line of (a) with the X-axis₄₀Is through the center of the inner circle of revolution and the center O of outer rotor 20₂Angle (X) to the X-axis₃₀，Y₃₀) Is the coordinate of the cycloid curve formed by the outer rolling circle, (X)₄₀，Y₄₀) Is the coordinate of the cycloid curve formed by the inner rolling circle.

In addition, the tooth space circle B is maintained₁Radius R of_b+2R_b1And addendum circle B₂Radius R of_b-2R_b2While the tooth profile U is deformed at a predetermined deformation rate in the circumferential direction_C. In FIG. 6, at the base radius R_bOutside of (i.e. gullet shape U)_3CIn the case of the' deformation, the 3 rd deformation rate delta₃＝θ_3C/θ_3C' deformation is carried out at the base radius R_bInner side of (i.e. addendum shape U)_4CIn the case of the' deformation, the 4 th deformation rate delta₄＝θ_4C/θ_4C' deformation is performed. In addition, the angle θ_3CEtc., as in the case of the inner rotor. The deformed tooth shape U is obtained by the deformation in the circumferential direction_C(gullet shape U)_3CAnd tooth tip shape U_4C). If the number of teeth of the outer rotor before and after the deformation in the circumferential direction is (n '+ 1) and (n +1), respectively, the relational expression (n' +1) × (θ)_3C’+θ_4C’)＝(n+1)×(θ_3C+θ_4C) This is true.

Here for forming a tooth profile U_C' obtaining a tooth-like shape U_COf transformation (e.g. toThe description of the inner rotor shows that the deformation ratio δ can be used₃Or delta₄But is simply shown. For example, the spline shape is a spline shape U before deformation in the circumferential direction_3C' is the cycloid curve (X)₃₀，Y₃₀) Tooth space shape U after deformation in circumferential direction_3CCoordinate (X) of₃₁，Y₃₁) These compounds may be represented by the following formulae (46) to (49).

R₃₁＝(X₃₀ ²+Y₃₀ ²)^1/2Formula (46)

θ₃₁＝arccos(X₃₀/R₃₁) Formula (47)

X₃₁＝R₃₁×cos(θ₃₁×δ₃) Formula (48)

Y₃₁＝R₃₁×sin(θ₃₁×δ₃) Formula (49)

Here, R is₃₁Is from the center O of the outer rotor₂To the coordinate (X)₃₀，Y₃₀) A distance of (a), theta₃₁Is through the center O of the outer rotor₂And coordinates (X)₃₀，Y₃₀) Is at an angle to the X-axis.

Due to the tooth crest shape U after deformation in the circumferential direction_4CCoordinate (X) of₄₁，Y₄₁) The tooth crest shape U before deformation in the circumferential direction may be used_4C', i.e. the cycloid curve (X) described above₄₀，Y₄₀) By using the deformation ratio delta₄Since it is also easy to obtain, it is omitted here.

Next, the tooth profile U after the deformation in the circumferential direction is treated_CThe deformation in the radial direction is performed as shown in fig. 7. First, will be satisfying R_b+2R_b1＞R_D3≥R_b≥R_D4＞R_b-2R_b2Radius R of_D3Circle D of₃The outer side (tooth groove side) of (c), as shown in fig. 7(a), coordinates represented by the following formulae (9) to (12) (a)X₃₂，Y₃₂) The formed curve is the tooth space shape after deformation.

R₃₂＝(X₃₁ ²+Y₃₁ ²)^1/2Formula (9)

θ₃₂＝arccos(X₃₁/R₃₂) Formula (10)

X₃₂＝{(R₃₂-R_D3)×β₃₀+R_D3}×cos θ₂₂Formula (11)

Y₃₂＝{(R₃₂-R_D3)×β₃₀+R_D3}×sin θ₂₂Formula (12)

Here, (X)₃₁，Y₃₁) Is in the form of tooth socket U before radial deformation_3C(X) of (C)₃₂，Y₃₂) Is in the form of tooth socket U after being deformed radially_3outCoordinate of (A), R₃₂Is from the center O of the outer rotor₂To the coordinate (X)₃₁，Y₃₁) A distance of (a), theta₃₂Is through the center O of the outer rotor₂And coordinates (X)₃₁，Y₃₁) Angle beta of the straight line of (A) to the X-axis₃₀Is a correction factor for the deformation.

In addition, R will be satisfied_b+2R_b1＞R_D3≥R_b≥R_D4＞R_b-2R_b2Radius R of_D4Circle D of₄Inner side (tooth top side) of (b), as shown in fig. 7(b), coordinates (X) represented by the following formulae (13) to (16)₄₂，Y₄₂) The formed curve is the tooth crest shape after deformation.

R₄₂＝(X₄₁ ²+Y₄₁ ²)^1/2Formula (13)

θ₄₂＝arccos(X₄₁/R₄₂) Formula (14)

X₄₂＝{R_D4-(R_D4-R₄₂)×β₄₀}×cos θ₄₂Formula (15)

Y₄₂＝{R_D4-(R_D4-R₄₂)×β₄₀}×sin θ₄₂Formula (16)

Here, (X)₄₁，Y₄₁) Is in the shape of tooth top U before radial deformation_4C(X) of (C)₄₂，Y₄₂) Is in the shape of tooth top U after being deformed in radial direction_4outCoordinate of (A), R₄₂Is from the center O of the outer rotor₂To the coordinate (X)₄₁，Y₄₁) A distance of (a), theta₄₂Is through the center O of the outer rotor₂And coordinates (X)₄₁，Y₄₁) Angle beta of the straight line of (A) to the X-axis₄₀Is a correction factor for the deformation.

Further, the outer rotor 20 and the inner rotor 10 satisfy the relationships of equations (17) to (21).

R_a＝n×(R_a1×γ₁+R_a2×γ₂) Formula (17)

R_b＝(n+1)×(R_b1×δ₃+R_b2×δ₄) Formula (18)

R_b＝R_a+R_a1+R_a2+ H1 type (19)

R_b2＝R_a2+ H2 type (20)

e₁₀＝R_a1+R_a2+ H3 type (21)

Here, e₁₀Is the center O of the inner rotor₁And center O of outer rotor₂The distances (eccentricity) H1, H2, and H3 are correction values for rotating the outer rotor with a gap therebetween.

That is, the radial deformation shown in FIG. 7(a) is caused by the spline shape U_3CObtain the tooth socket shape U_3outBy the deformation in the radial direction shown in FIG. 7(b), the tooth top shape U is formed_4CObtain the tooth top shape U_4out. As described above, by performing the above-described deformation in the circumferential direction and the deformation in the radial direction on the tooth profile U' formed of the cycloid curve, the tooth profile U of the outer rotor formed of the deformed cycloid curve can be obtained_out(gullet shape U)_3outAnd tooth tip shape U_4out) The internal tooth shape of the outer rotor 20 shown in fig. 3 can be formed.

The formation of the inner rotor 10 and the outer rotor 20 may be subjected to various conditions and modifications described in the description of fig. 1 and 2.

[ case of tooth shapes made of other mathematical curves ]

The mathematical curve in the present invention is not limited to a cycloid curve, of course. In addition, as the mathematical curve, for example, an envelope curve of an arc group having a center on a trochoid curve or an arc curve formed by 2 arcs connecting a tooth top portion and a tooth space portion to each other may be used.

The tooth profile of the present invention can be obtained by performing the deformation in the circumferential direction and the deformation in the radial direction described in fig. 1 and 2 on the tooth profile formed by the envelope curve of the arc group having the center on the trochoid curve or the arc curve formed by 2 arcs connecting the tooth top portion and the tooth space portion. In this case, various conditions and changes described in the description of fig. 1 and 2 may be applied.

Fig. 8 and 9 show the tooth profile before the above-described deformation in the circumferential direction and the deformation in the radial direction, that is, the tooth profile formed by a mathematical curve. Fig. 8 a shows the tooth profile (external tooth profile) of the inner rotor before deformation, which is formed by the envelope of the arc group having the center on the trochoid curve, and fig. 8 b shows the tooth profile (internal tooth profile) of the outer rotor meshing with the inner rotor before deformation.

In fig. 8(a), the tooth profile U of the inner rotor before deformation is formed_TinThe coordinates of the envelope of the known circular arc group having the center on the trochoid curve are represented by the following equations (51) to (56). In addition, in fig. 8(a), the addendum circle a₁And the tooth space circle A₂Respectively with R_A1And R_A2And (4) showing.

X₁₀₀＝(R_H+R_I)×cos θ₁₀₀-e_K×cos θ₁₀₁Formula (51)

Y₁₀₀＝(R_H+R_I)×sin θ₁₀₀-e_K×sin θ₁₀₁Formula (52)

θ₁₀₁＝(n+1)×θ₁₀₀Formula (53)

R_H＝n×R_IFormula (54)

X₁₀₁＝X₁₀₀±R_J/{1+(dX₁₀₀/dY₁₀₀)²}^1/2Formula (55)

Y₁₀₁＝Y₁₀₀±R_J/{1+(dY₁₀₀/dX₁₀₀)²}^1/2Formula (56)

Here, the center O of the inner rotor is passed through₁Is the X axis such that the straight line orthogonal to the X axis passes through the center O of the inner rotor₁Is the Y axis, and in the formulae (51) to (56), (X)₁₀₀，Y₁₀₀) Is the coordinate on the trochoid curve T, R_HIs the radius of the base circle of the trochoid, R_IIs the radius of the trochoid generating circle, e_KIs the center O of the trochoid generating circle_TAnd the distance, theta, between the points at which the trochoid curve T is generated₁₀₀Is passing through the center O of the trochoid generating circle_TAnd the center O of the inner rotor₁Is a straight line ofAngle of X-axis, theta₁₀₁Is passing through the center O of the trochoid generating circle_TAnd the angle formed by the straight line of the point generating the trochoid curve T and the X axis, (X)₁₀₁，Y₁₀₁) Is the coordinate on the envelope, R_JIs an arc C forming an envelope_EOf (c) is used.

In addition, the tooth profile U of the outer rotor before deformation shown in fig. 8(b)_ToutThe arc curves of' are represented by the following formulae (57) to (60). In addition, in fig. 8(B), a spline circle B₁And addendum circle B₂Respectively with R_B1And R_B2And (4) showing.

(X₂₀₀-X₂₁₀)²+(Y₂₀₀-Y₂₁₀)²＝R_J ²Formula (57)

X₂₁₀ ²+Y₂₁₀ ²＝R_L ²Formula (58)

X₂₂₀ ²+Y₂₂₀ ²＝R_B1 ²Formula (59)

R_B1＝(3×R_A1-R_A2)/2+g₁₀Formula (60)

Here, the center O of the outer rotor is passed through₂Is X-axis, is orthogonal to the X-axis and passes through the center O of the outer rotor₂Is the Y axis, and in the formulae (57) to (60), (X)₂₀₀，Y₂₀₀) Is the coordinate of the arc forming the tip of the tooth, (X)₂₁₀，Y₂₁₀) Is the coordinate of the center of the circle whose arc-shaped tooth-forming tip is rounded, (X)₂₂₀，Y₂₂₀) Is a tooth space circle B forming a tooth space part₁Coordinates of the arc of (1), R_LIs the center O of the outer rotor₂And the center of the circle of its circular arc-shaped tooth-forming top, R_B1Is a tooth space circle B forming a tooth space part₁Radius of (g)₁₀Is a correction value for rotating the outer rotor with a gap.

Fig. 9 a shows the tooth profile (external tooth profile) of the inner rotor before deformation, which is formed by an arc curve formed by 2 arcs connecting the tooth top and the tooth space, and fig. 9 b shows the tooth profile (internal tooth profile) of the outer rotor meshing with the inner rotor before deformation.

In fig. 9(a), the tooth profile U of the inner rotor before deformation is formed_SinThe coordinates of the well-known circular arc curves represented by 2 circular arcs where the tooth top portion and the tooth groove portion meet each other are represented by the following equations (71) to (76). In addition, in fig. 9(a), the addendum circle a₁And the tooth space circle A₂Respectively with R_A1And R_A2And (4) showing.

(X₅₀-X₆₀)²+(Y₅₀-Y₆₀)²＝(r₅₀+r₆₀)²Formula (71)

X₆₀＝(R_A2+r₆₀)×cos θ₆₀Formula (72)

Y₆₀＝(R_A2+r₆₀)×sin θ₆₀Formula (73)

X₅₀＝R_A1-r₅₀Formula (74)

Y

₅₀0 type (75)

θ₆₀Pi/n type (76)

Here, the center O of the inner rotor is passed through₁Is the X axis such that the straight line orthogonal to the X axis passes through the center O of the inner rotor₁Is the Y axis, (X)₅₀，Y₅₀) Is the coordinate of the center of the arc forming the tip of the tooth, (X)₆₀，Y₆₀) Is the coordinate of the center of the arc forming the tooth space, r₅₀Formed with tooth topsRadius of circular arc, r₆₀Is the radius of the arc forming the tooth groove part, theta₆₀Is passed through the center of the arc forming the tooth tip and the center O of the inner rotor₁And a center of an arc passing through the tooth groove portion and a center O of the inner rotor₁Angle of the straight line of (a).

In addition, the tooth profile U of the outer rotor before deformation shown in fig. 9(b)_SoutThe arc curves of' are represented by the following formulae (77) to (82). In addition, in FIG. 9(B), the spline circle B₁And addendum circle B₂Respectively with R_B1And R_B2And (4) showing.

(X₇₀-X₈₀)²+(Y₇₀-Y₈₀)²＝(r₇₀+r₈₀)²Formula (77)

X₈₀＝(R_B2+r₈₀)×cos θ₈₀Formula (78)

Y₈₀＝(R_B2+r₈₀)×sin θ₈₀Formula (79)

X₇₀＝R_B1-r₇₀Formula (80)

Y

₇₀0 type (81)

θ₈₀Pi/(n +1) formula (82)

Here, the center O of the outer rotor is passed through₂Is X-axis, is orthogonal to the X-axis and passes through the center O of the outer rotor₂Is the Y axis, (X)₇₀，Y₇₀) Is the coordinate of the center of the arc forming the tooth groove part, (X)₈₀，Y₈₀) Is the coordinate of the center of the arc forming the tooth tip, r₇₀Is the radius of the arc forming the tooth groove portion, r₈₀Is the radius of the arc forming the tooth tip, θ₈₀Through an arc forming the top of the toothCenter and center of outer rotor O₂And a straight line passing through the center of the arc forming the tooth groove portion and the center O of the outer rotor₂Angle of the straight line of (a).

[ case of tooth shape after second deformation in radial direction ]

The tooth profile of the tooth top portion of the inner rotor obtained in the embodiment described above is further modified in the second radial direction, which is also one of preferred embodiments of the present invention. Next, a second modification in the radial direction will be described with reference to fig. 10 and 11.

Fig. 10 is an explanatory diagram of a method of determining a reference point for performing the second modification. The oil pump rotor shown in the figure is formed by deforming a tooth profile shape formed by a mathematical curve in a circumferential direction and in a radial direction, and maintains an addendum circle a when deforming in the circumferential direction₁Radius R of_A1And the tooth space circle A₂Radius R of_A2The distance between them. The meshing region is determined based on the tooth shapes of the inner rotor 10 and the outer rotor 20. For example, in the example of the oil pump shown in fig. 10, a curve connecting the tooth-space-side meshing point b and the tooth-top-side meshing point a is a region where the inner rotor 10 and the outer rotor 20 mesh with each other. That is, when the inner rotor 10 rotates, the inner rotor 10 and the outer rotor 20 start to mesh at the tooth-groove-side meshing point b among the 1 outer teeth 11a (fig. 10 (a)). Then, the meshing point gradually slides toward the tooth crest side of the outer teeth 11a, and finally the inner rotor 10 and the outer rotor 20 are no longer meshed at the tooth crest side meshing point a (fig. 10 (b)).

In fig. 10, the tooth crest side meshing point a and the tooth trough side meshing point b are shown only for the tooth crest portion of 1 outer tooth 11a out of the outer teeth 11 formed on the inner rotor 10, and the other teeth are omitted.

Fig. 11 is an explanatory diagram for explaining a second modification in the radial direction. In fig. 11, among the tooth profile shapes formed by mathematical curves, the tooth profile U after the tooth tip shape is deformed in the circumferential direction is shown by a broken lineNote that, the tooth shape U after the radial deformation (hereinafter, referred to as a first deformation for convenience of explanation) is shown_inIndicated by a solid line. For the tooth profile shape U and the tooth profile shape U_inThe modification (2) is as already described with reference to fig. 1 and 2. In fig. 11, it is further shown that the radius through the addendum-side meshing point a of the inner rotor is R_αCircle C of_α。

In a second radial variation, circle C_αThe tooth shape U after the first deformation is used as a reference circle_inReference circle C in_αThe tooth crest portion on the outer side of (2) is deformed at a deformation ratio epsilon. Here, the deformation ratio ∈ is a constant satisfying 0 < ∈ < 1, and the second deformation is a deformation that always extends radially inward. By the second deformation in the radial direction, the deformed tooth shape U shown by the thick solid line in fig. 11 can be obtained_in2. The reference circle C of the inner rotor obtained in the above manner passing through the tooth tip side meshing point a_αTooth profile shape U of the outer tooth top_in2The curves formed by equations (83) to (86) are referred to as tooth shapes.

R₄₀₀＝(X₃₀₀ ²+Y₃₀₀ ²)^1/2Formula (83)

θ₄₀₀＝arccos(X₃₀₀/R₄₀₀) Formula (84)

X₄₀₀＝{(R₄₀₀-R_α)×ε+R_α}×cos θ₄₀₀Formula (85)

Y₄₀₀＝{(R₄₀₀-R_α)×ε+R_α}×sin θ₄₀₀Formula (86)

Here, (X)₃₀₀，Y₃₀₀) Is in the shape of tooth top U after first deformation in radial direction_in(X) of (C)₄₀₀，Y₄₀₀) The tooth crest shape U is formed by second deformation in the radial direction_in2Coordinate of (A), R₄₀₀Is from the center O of the inner rotor₁To the coordinate (X)₃₀₀，Y₃₀₀) A distance of (a), theta₄₀₀Is through the center O of the inner rotor₁And coordinates (X)₃₀₀，Y₃₀₀) Is at an angle to the X-axis.

In fig. 11, only 1 tooth top portion of the outer teeth formed on the inner rotor is shown, and other teeth are omitted, but it goes without saying that the same modification is performed for all the teeth.

Fig. 12 is a graph showing a change in the tooth tip clearance accompanying the rotation of the inner rotor. In this example, data is shown, as an example, in a case where the reference circle C passing through the tooth crest side meshing point a of the inner rotor is further formed after the cycloid curve is deformed in the circumferential direction and the radial direction_αThe outer tooth crest portion of (2) is deformed at a deformation ratio ∈ of 0.5. In the graph, the rotation angle of the inner rotor is based on a position where both the tooth groove portion of the inner rotor and the tooth groove portion of the outer rotor are aligned on the axis O of the inner rotor, which is eccentric to each other₁And the axis O of the outer rotor₂Position on the straight line of the connection.

In this way, the tooth profile before the second deformation in the radial direction changes in a trigonometric function with the rotation of the inner rotor so that the tooth tip clearance becomes maximum when the rotation angle of the inner rotor is 0 degrees and becomes minimum when the half tooth amount is rotated. On the other hand, with the tooth profile shape after the second deformation, the tip clearance is kept constant regardless of the rotation angle of the inner rotor. Therefore, the tooth profile shape after the second deformation in the radial direction stabilizes the amount of oil leakage between the tooth tips of the inner rotor 10 and the outer rotor 20, and therefore pulsation of oil discharged from the oil pump can be suppressed to a lower level.

[ case of compression deformation in the circumferential direction ]

In each of the above configurations, the outer tooth shape of the inner rotor is formed by deforming the tooth profile formed by the mathematical curve in the circumferential direction and deforming the tooth profile in the radial direction. By performing the deformation in the circumferential direction and the deformation in the radial direction as described above, the discharge amount can be increased without increasing the size of the rotor (suppressing the increase in the size), and a low-noise oil pump rotor with a small pulsation can be provided in which the number of teeth is increased, but even if the compression deformation is performed only in the circumferential direction as described above, the discharge amount can be increased while the diameter of the rotor is secured, and a low-noise oil pump rotor with a small pulsation and an increased number of teeth can be provided.

In this case, the tooth crest shape and the tooth groove shape may be formed at the same deformation ratio (γ in fig. 1)₁＝γ₂) A structure for performing the deformation. It is needless to say that the same modification can be applied to the outer rotor.

[ other embodiments of the tooth shape of the outer rotor ]

As described in the above embodiment, the outer rotor appropriately meshing with the inner rotor having the outer tooth shape in which various modifications are made to the tooth profile shape formed by the mathematical curve while maintaining the addendum circle a may be formed by performing the same modification to the outer rotor in accordance with the modification of the inner rotor, but may be formed as described in another embodiment described below₁Radius R of_A1And the tooth space circle A₂Radius R of_A2The distance between them is simultaneously deformed in the circumferential direction and radially, or compressed in the circumferential direction. This can be applied to any inner rotor, and this embodiment will be described in detail with reference to fig. 13.

As shown in fig. 13(a), first, the center O of the inner rotor 10 is passed through₁Is the X-axis such that the straight line orthogonal to the X-axis passes through the center O of the inner rotor 10₁The straight line of (2) is the Y axis and is the center O of the inner rotor 10₁As the origin. Further, the center O of the inner rotor 10 is set as₁Coordinates (e, 0) are acquired from a position a predetermined distance e, and a circle with a radius e and centered at the coordinates (e, 0) is defined as a circle F.

First, ifMake the center O of the inner rotor 10₁When the envelope Z revolves clockwise at an angular velocity ω along the circumference of the circle F and rotates counterclockwise at an angular velocity ω/n (n is the number of inner rotor teeth), as shown in fig. 13(a), the envelope Z can be formed₀. In fig. 13, the center O of the inner rotor 10 at the time of starting the revolution as viewed from the center (e, 0) of the circle F₁The angle of (d), i.e., the negative direction of the X axis, is set as the revolution angle 0 direction, and the revolution angle is acquired so as to increase in value with respect to the clockwise rotation.

Here, for the envelope Z₀The operation is performed so as to obtain a curve in which at least the envelope Z is set₀And near the intersection part of the axis in the revolution angle 0 direction, deforming the envelope Z in the outer diameter direction₀And revolution angle theta₂In the vicinity of the intersection of the axis in the direction of (═ pi/(n +1)), the deformation in the outer diameter direction is smaller than or equal to the deformation in the vicinity of the intersection of the axis in the direction of the revolution angle 0.

As described above, the center O of the inner rotor 10 is set to be the center O₁When revolving while rotating along the circumference of the circle F, the revolution angle is greater than or equal to 0 and less than or equal to theta₁The tooth crest shape of the inner rotor 10 is expanded by the correction coefficient beta₁Deformed in the outer radial direction and has a revolution angle of theta or more₁During the period of 2 pi, the tooth top shape of the inner rotor 10 is expanded by the correction coefficient beta₂Deforming in the direction of the outer diameter. However, in the present embodiment, the coefficient β is corrected for expansion₂Value of (d) and expansion correction coefficient beta₁The case of (b) is relatively small, but the expansion correction coefficient β is small₂Value of (d) and dilation correction factor β₁The value of (b) may be arbitrarily set without being obtained according to the relationship.

Since by the above operation, as shown in fig. 13(a), the inner rotor 10 is located at the broken line I₀At the position of (2), using the expansion correction coefficient beta₁Deformed in the direction of the outer diameter, at the position of the dotted line I₁At the position of (2), using the expansion correction coefficient beta₂To and β₁Is deformed in the outer diameter direction in a smaller manner than in the case of (1), so the envelope Z obtained in this case₁Is in the shape of the envelope Z₀In contrast, the vicinity of the intersection with the axis in the direction of the revolution angle 0 is deformed in the outer diameter direction and also deformed in the revolution angle θ₂The vicinity of the intersection of the axes in the direction is deformed in the outer diameter direction less than the deformation in the outer diameter direction in the vicinity of the intersection of the axes in the revolution angle 0 direction. Furthermore, the expansion correction coefficient beta is used₂Value of (d) and expansion correction coefficient beta₁Is deformed equally in the outer radial direction when the values of (a) and (b) are equal.

Then, as shown in fig. 13(b), at the envelope Z₁In the revolution angle of more than or equal to 0 and less than or equal to theta₂Is determined (revolution angle 0 direction axis and revolution angle theta)₂The region between the axes of the directions) as a partial envelop PZ₁And extracted.

And, extracting partial envelope PZ₁A part extending to the outside of the region W by the rotation is cut off while rotating by a minute angle alpha in the revolution direction with the center (e, 0) of the circle F as a base point, and is connected to a partial envelop PZ₁Forming a correction partial envelop MZ with a gap G between the rotor and the axis in the revolution angle 0 direction₁. In the present embodiment, the gaps G are connected in a straight line, but the gaps G are not limited to a straight line and may be connected in a curved line.

In addition, the correction part is wrapped by the MZ₁The partial tooth profile PT is formed by axially symmetrically transferring the tooth profile PT with respect to the axis in the revolution angle 0 direction, and the tooth profile of the outer rotor 20 is formed by rotationally transferring the partial tooth profile PT at an angle of 2 pi/(n +1) with the center (e, 0) of the circle F as a base point.

By using envelope Z₀Envelope Z of the above-described configuration after deformation₁Forming the outer rotor can ensure an appropriate gap between the inner rotor 10 and the outer rotor 20. In addition, by partially enveloping PZ₁Is made tinyThe appropriate backlash can be obtained by rotating the angle α. This makes it possible to obtain the outer rotor 20 that rotates while smoothly meshing with the deformed inner rotor 10.

[ other embodiments ]

In each of the above embodiments, the outer tooth shape (inner tooth shape) of the inner rotor 10 (outer rotor 20) in the oil pump rotor is formed by performing deformation in the circumferential direction and deformation in the radial direction or compression deformation in the circumferential direction with respect to the tooth profile shape formed by the mathematical curve, but the outer tooth shape (inner tooth shape) of the inner rotor 10 (outer rotor 20) may be formed by performing deformation only in the radial direction. The deformation in the radial direction is not limited to the deformation on both the tooth top side and the tooth slot side, and may be the deformation on either the tooth top side or the tooth slot side.

Industrial applicability

The present invention can be applied to an oil pump rotor that sucks and discharges fluid by utilizing a volume change of a chamber formed between an inner rotor and an outer rotor.

Claims

1. An oil pump rotor for use in an oil pump, the oil pump having:

an inner rotor forming n outer teeth, wherein n is a natural number;

an outer rotor that forms n +1 inner teeth that mesh with the outer teeth; and

a housing having a suction port for sucking fluid and a discharge port for discharging fluid,

when the two rotors are engaged and rotated, a fluid is sucked and discharged by a volume change of a chamber formed between tooth surfaces of the two rotors to transfer the fluid,

it is characterized in that the preparation method is characterized in that,

the outer tooth shape of the inner rotor is formed by deforming a tooth shape formed by a mathematical curve in a circumferential direction and deforming the tooth shape in a radial direction, and the addendum circle A is maintained when the deformation in the circumferential direction is performed₁Radius R of_A1And the tooth space circle A₂Radius R of_A2The distance between them.

2. The oil pump rotor as set forth in claim 1,

the mathematical curve is any one of a cycloid curve, an envelope curve of an arc group having a center on a trochoid curve, or an arc curve formed by 2 arcs in which a tooth top portion and a tooth groove portion are in contact with each other.

3. The oil pump rotor as set forth in claim 1,

the deformation in the circumferential direction satisfies R_A1＞R_C1＞R_A2Radius R of_C1Circle C of₁At a1 st deformation rate gamma₁Is deformed while being on the circle C₁At a2 nd deformation rate gamma₂The deformation is carried out, and the deformation is carried out,

said deformation in the radial direction being such as to satisfy R_A1＞R_D1≥R_C1≥R_D2＞R_A2Radius R of_D1Circle D of₁The tooth crest shape is a curve formed by the equations (1) to (4) and has a radius R_D2Circle D of₂In the case of deforming the inner side of (2), the curve formed by the equations (5) to (8) is defined as a tooth space shape,

R₁₂＝(X₁₁ ²+Y₁₁ ²)^1/2formula (1)

θ₁₂＝arccos(X₁₁/R₁₂) Formula (2)

X₁₂＝{(R₁₂-R_D1)×β₁₀+R_D1}×cosθ₁₂Formula (3)

Y₁₂＝{(R₁₂-R_D1)×β₁₀+R_D1}×sinθ₁₂Formula (4)

Wherein,

β₁₀is a correction factor for the deformation and,

R₂₂＝(X₂₁ ²+Y₂₁ ²)^1/2formula (5)

θ₂₂＝arccos(X₂₁/R₂₂) Formula (6)

X₂₂＝{R_D2-(R_D2-R₂₂)×β₂₀}×cosθ₂₂Formula (7)

Y₂₂＝{R_D2-(R_D2-R₂₂)×β₂₀}×sinθ₂₂Formula (8)

Wherein,

β₂₀is a correction factor for the deformation.

4. The oil pump rotor as set forth in claim 1,

a reference circle C of the inner rotor passing through a tooth crest side meshing point a of the outer rotor_αThe tooth crest portion of the outer side of the tooth is deformed in the radial direction at a deformation rate ε satisfying 0 < ε < 1.

5. The oil pump rotor as set forth in claim 3,

the outer tooth shape of the inner rotor is formed by matching a base circle with a radius of R_aThe radius of the outer rolling circle is R_a1The radius of the inner rolling circle is R_a2The tooth profile of the cycloid curve is formed by performing the deformation in the circumferential direction and the deformation in the radial direction, and when the deformation in the circumferential direction is performed, a base circle of the cycloid curve is defined as the circle C₁，

the radial deformation of the outer rotor satisfies R_B1＞R_D3≥R_b≥R_D4＞R_B2Radius R of_D3Circle D of₃In the case of the outer side deformation, the curve formed by the equations (9) to (12) is formed into a tooth space shape at the radius R_D4Circle D of₄In the case of the inner side of (2), the following formulas (13) to (b)16) The formed curve is used as the tooth top shape,

and the outer rotor and the inner rotor satisfy the relationship of equations (17) to (21),

R₃₂＝(X₃₁ ²+Y₃₁ ²)^1/2formula (9)

θ₃₂＝arccos(X₃₁/R₃₂) Formula (10)

X₃₂＝{(R₃₂-R_D3)×β₃₀+R_D3}×cosθ₃₂Formula (11)

Y₃₂＝{(R₃₂-R_D3)×β₃₀+R_D3}×sinθ₃₂Formula (12)

Wherein,

β₃₀is a correction factor for the deformation and,

R₄₂＝(X₄₁ ²+Y₄₁ ²)^1/2formula (13)

θ₄₂＝arccos(X₄₁/R₄₂) Formula (14)

X₄₂＝{R_D4-(R_D4-R₄₂)×β₄₀}×cosθ₄₂Formula (15)

Y₄₂＝{R_D4-(R_D4-R₄₂)×β₄₀}×sinθ₄₂Formula (16)

Wherein,

(X₄₁，Y₄₁) The tooth crest shape being before radial deformationThe coordinates of the position of the object to be imaged,

(X₄₂，Y₄₂) Is the coordinate of the tooth crest shape after the radial deformation,

β₄₀is a correction factor for the deformation and,

in addition, the first and second substrates are,

R_a＝n×(R_a1×γ₁+R_a2×γ₂) Formula (17)

R_b＝(n+1)×(R_b1×δ₃+R_b2×δ₄) Formula (18)

R_b＝R_a+R_a1+R_a2+ H1 type (19)

R_b2＝R_a2+ H2 type (20)

e₁₀＝R_a1+R_a2+ H3 type (21)

Wherein,

e₁₀is the distance between the center of the inner rotor and the center of the outer rotor, i.e. the amount of eccentricity,

h1, H2, and H3 are correction values for rotating the outer rotor with a gap.

6. An oil pump rotor for use in an oil pump, the oil pump having:

an inner rotor forming n outer teeth, wherein n is a natural number;

an outer rotor that forms n +1 inner teeth that mesh with the outer teeth; and

a housing which forms a suction port for sucking fluid and a discharge port for discharging fluid,

it is characterized in that the preparation method is characterized in that,

the outer tooth profile of the inner rotor is formed by performing compression deformation in the circumferential direction while maintaining the distance between the radius RA1 of the addendum circle a1 and the radius RA2 of the spline circle a2, in a tooth profile shape formed by a mathematical curve.

7. The oil pump rotor as claimed in claim 1 or 6,

the outer rotor engaged with the inner rotor has a tooth shape formed in such a manner that: